As in [1]}, if \(J\)  is a small category and \(F\colon J\rightarrow \Delta ^\mathrm {op}\)  is a functor we define the generalized latching object \(L_JX\)  of a simplicial object \(X\)  to be the colimit
\(L_J X = \operatornamewithlimits{\mathrm {colim}}_J X\) 
